## Annals of Mathematics |

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abelian variety arbitrary arithmetically effective assume automorphism base points bundle Cm-diffeomorphism coefficients cohomology commutative compact completes the proof complex consider constant contains continuous pseudogroup Corollary corresponding curve decomposition Definition deformation denote diffeomorphism differential forms differential operator dimension direct sum divisor effective cycle element equivalent exact sequence exists fibre fixed component follows formula functional equation G-module germs graded Lie algebra group G Hence homomorphism homotopy ideal identity imbedded implies indecomposable induced integer invariant irreducible isomorphic kernel knot Let G Lie algebra Lie group linear system manifold Math matrix modules neighborhood non-singular notation obtain orientable orthogonal Poincare lemma polynomial prime components principal bundle projection proof of Theorem Proposition prove pseudogroup rational real numbers regular neighborhood representation respectively ring s(nD satisfies Seifert matrix sheaf singular solvmanifold subgroup subset subspace supp Suppose symmetric T-coordinate Theorem 3.1 topological transformations vector bundle vector space zero